Three-dimensional mapping using scanning electron microscope images

ABSTRACT

A method includes irradiating a surface of a sample, which is made-up of multiple types of materials, with a beam of primary electrons. Emitted electrons emitted from the irradiated sample are detected using multiple detectors that are positioned at respective different positions relative to the sample, so as to produce respective detector outputs. Calibration factors are computed to compensate for variations in emitted electron yield among the types of the materials, by identifying, for each material type, one or more horizontal regions on the surface that are made-up of the material type, and computing a calibration factor for the material type based on at least one of the detector outputs at the identified horizontal regions. The calibration factors are applied to the detector outputs. A three-dimensional topographical model of the surface is calculated based on the detector outputs to which the calibration factors are applied.

RELATED APPLICATIONS

This patent application is a continuation of U.S. patent applicationSer. No. 14/081,981 filed on Nov. 15, 2013, which is a continuation ofU.S. patent application Ser. No. 13/365,238 filed on Feb. 2, 2012, nowU.S. Pat. No. 8,604,427, all of which are incorporated by referenceherein.

TECHNICAL FIELD

Embodiments of the present invention relates generally to processing ofScanning Electron Microscope (SEM) images, and particularly to methodsand systems for three-dimensional mapping using SEM images.

BACKGROUND

Scanning Electron Microscope (SEM) images are used in various mappingand imaging applications, such as for inspection of semiconductorwafers. Several techniques are known in the art for three-dimensional(3D) mapping of samples using SEM images. For example, a conventionaltechnique for inspecting semiconductor devices utilizes multiple sets ofmeasurement data obtained by a SEM to determine the dimensionalparameters of a semiconductor device. The SEM collects each set of datafrom a different angular orientation with respect to the device. Thedimensional parameters of the semiconductor device are determined byanalyzing the relationship between the SEM inspection angle and thecollected data sets.

Another conventional method includes a 3D shape measurement in whichdetection signals from respective semiconductor elements aresequentially switched in synchronization with a scanning frame of anelectron beam on a sample. The detection signals from the respectivesemiconductor elements can be sequentially recorded in recordingaddresses in a frame memory that correspond to the respectivesemiconductor elements. After four electron beam scanning sessions, eachimage data for 3D shape measurement is recorded in the frame memory, andprocessed for 3D shape measurement.

As yet another example, Marinello et al., describes dimensionalmeasurements performed with a SEM using 3D reconstruction of surfacetopography through stereo-photogrammetry, in “Critical Factors in SEM 3DStereo Microscopy,” Measurement Science and Technology, volume 19, no.6, 2008, which is incorporated herein by reference.

Some conventional SEM mapping techniques use multiple detectors. Forexample, Harada et al. describe multi-detector SEM measurements in “ANew CDSEM Metrology Method for Thin Film Hardmasks Patterns usingMultiple Detectors,” Photomask Japan 2010 (published in BACUS News 27:2,February, 2011).

SUMMARY

A method includes irradiating a surface of a sample, which is made-up ofmultiple types of materials, with a beam of primary electrons. Emittedelectrons emitted from the irradiated sample are detected using multipledetectors that are positioned at respective different positions relativeto the sample, so as to produce respective detector outputs. Calibrationfactors are computed to compensate for variations in emitted electronyield among the types of the materials, by identifying, for eachmaterial type, one or more horizontal regions on the surface that aremade-up of the material type, and computing a calibration factor for thematerial type based on at least one of the detector outputs at theidentified horizontal regions. The calibration factors are applied tothe detector outputs. A three-dimensional topographical model of thesurface is calculated based on the detector outputs to which thecalibration factors are applied.

In some embodiments, the detectors include a top detector that ispositioned perpendicularly above a plane of the sample, and two or moreside detectors that are positioned at oblique angles relative to theplane of the sample. In an embodiment, identifying the horizontalregions includes segmenting the surface into multiple segments made-upof the respective types of the materials, and identifying one or more ofthe horizontal regions within each of the segments.

In one embodiment, calculating the three-dimensional topographical modelincludes estimating height gradients at multiple points on the surface,and integrating the height gradients to produce the three-dimensionaltopographical model. Estimating the height gradients may includedefining, for a given point on the surface, a set of equations thatexpress the detector outputs as a function of respective reflectancefunctions, and deriving a height gradient at the given point by solvingthe set of the equations. In an embodiment, the method includesevaluating a reflectance function of a given detector by integrating anangular distribution of the emitted electron yield over a range ofangles captured by the given detector. Estimating the height gradientsmay include resolving an ambiguity in a component of the heightgradients by applying a criterion that requires an integral of theheight gradients over a closed loop path on the surface to be zero.

In some embodiments, applying the calibration factors includesnormalizing a reflectance function for a given detector, which isestimated at a point on the surface that is made-up of a material type,using a calibration factor computed for the material type. In anembodiment, the detectors include a top detector positionedperpendicularly above a plane of the sample, and four side detectorspositioned at oblique angles relative to the plane of the sample,detecting the emitted electrons includes combining the detector outputsof selected pairs of the side detectors, and calculating thethree-dimensional topographical model includes computing the model basedon the combined detector outputs.

There is additionally provided, in accordance with an embodiment of thepresent invention, an apparatus including an electron source, multipledetectors and a processor. The electron source is configured toirradiate a surface of a sample, which is made-up of multiple types ofmaterials, with a beam of primary electrons. The detectors arepositioned at respective different positions relative to the sample andare configured to detect emitted electrons that are emitted from theirradiated sample, so as to produce respective detector outputs. Theprocessor is configured to compute calibration factors to compensate forvariations in emitted electron yield among the types of the materials byidentifying, for each material type, one or more horizontal regions onthe surface that are made-up of the material type, and computing acalibration factor for the material type based on at least one of thedetector outputs at the identified horizontal regions, to apply thecalibration factors to the detector outputs, and to calculate athree-dimensional topographical model of the surface based on thedetector outputs to which the calibration factors are applied.

There is also provided, in accordance with an embodiment of the presentinvention, an apparatus including an interface and a processor. Theinterface is configured to receive multiple detector outputs fromrespective detectors positioned at respective different positionsrelative to a sample, which is made-up of multiple types of materials,wherein the detector outputs are indicative of emitted electrons thatare emitted from the sample in response to irradiation of the sample bya beam of primary electrons. The processor is configured to computecalibration factors to compensate for variations in emitted electronyield among the types of the materials by identifying, for each materialtype, one or more horizontal regions on the surface that are made-up ofthe material type, and computing a calibration factor for the materialtype based on at least one of the detector outputs at the identifiedhorizontal regions, to apply the calibration factors to the detectoroutputs, and to calculate a three-dimensional topographical model of thesurface based on the detector outputs to which the calibration factorsare applied.

There is further provided, in accordance with an embodiment of thepresent invention, a computer software product, the product including atangible non-transitory computer-readable medium, in which programinstructions are stored, which instructions, when read by a computer,cause the computer to receive multiple detector outputs from respectivedetectors positioned at respective different positions relative to asample, which is made-up of multiple types of materials, wherein thedetector outputs are indicative of emitted electrons that are emittedfrom the sample in response to irradiation of the sample by a beam ofprimary electrons, to compute calibration factors to compensate forvariations in emitted electron yield among the types of the materials byidentifying, for each material type, one or more horizontal regions onthe surface that are made-up of the material type, and computing acalibration factor for the material type based on at least one of thedetector outputs at the identified horizontal regions, to apply thecalibration factors to the detector outputs, and to calculate athree-dimensional topographical model of the surface based on thedetector outputs to which the calibration factors are applied.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will be more fully understood from the followingdetailed description of the embodiments thereof, taken together with thedrawings in which:

FIG. 1 is a block diagram that schematically illustrates a system forthree-dimensional (3D) mapping of samples, in accordance with anembodiment of the present invention;

FIG. 2 is a diagram that schematically illustrates a detector array, inaccordance with an alternative embodiment of the present invention;

FIGS. 3 and 4 are diagrams showing geometrical conventions used indescribing embodiments of the present invention;

FIG. 5 is a graph showing functions used in calculating a heightgradient map, in accordance with an embodiment of the present invention;and

FIGS. 6 and 7 are flow charts that schematically illustrate methods for3D mapping of samples, in accordance with embodiments of the presentinvention.

FIG. 8 is a block diagram illustrating one embodiment of a computersystem, according to an embodiment.

DETAILED DESCRIPTION Overview

Embodiments of the present invention provide methods and systems forcalculating a three-dimensional (3D) topographical model of a samplesurface from multiple Scanning Electron Microscope (SEM) images of thesample, captured by multiple detectors. In particular, a disclosedcalibration process prevents distortion of the 3D model when the samplesurface is made-up of multiple types of materials.

In some embodiments, the sample is irradiated with a beam of primaryelectrons. Multiple detectors, which are positioned at differentpositions relative to the sample, detect secondary and backscatteredelectrons that are emitted from the irradiated sample. For example, thedetectors may comprise a top detector that is positioned directly abovethe sample, plus two or more side detectors.

Each detector produces a respective detector output that is indicativeof the yield of secondary electrons captured by the detector. Aprocessor reconstructs a 3D topographical model of the sample byprocessing the multiple detector outputs. Typically, the processorestimates surface height gradients across the sample, and thenintegrates the gradients to produce the 3D topographical model.

In many practical applications, the sample surface is made-up ofmultiple types of materials. Unless accounted for, the differences inmaterial types may distort the 3D reconstruction, because the yield ofsecondary electrons in a particular direction depends not only on thesurface topography but also on its material composition.

In one embodiment, the processor computes calibration factors tocompensate for the variations in secondary electron yield among thedifferent material types. The processor applies the calibration factorsto the detector outputs in calculating the 3D topographical model of thesurface. In an example embodiment, the processor identifies, for eachmaterial type, one or more regions of the surface that are substantiallyhorizontal. The processor performs reference yield measurements for thedifferent material types at the horizontal regions, and uses thesemeasurements to compute the calibration factors. The processor thenapplies these calibration factors to the outputs of the detectors,produced in other regions of the sample. As a result, the 3Dtopographical model is unaffected by the different material types of thesample surface.

The methods and systems described herein produce highly-accurate 3Dmodels of samples, irrespective of the various material types that maybe present on the sample surface. The disclosed techniques can be usedin a variety of applications that examine samples having multiplematerials, such as in Critical Dimension (CD) measurements, DefectReview (DR) and Automatic Defect Classification (ADC) of semiconductorwafers.

System Description

FIG. 1 is a block diagram that schematically illustrates a ScanningElectron Microscope (SEM) system 20 for three-dimensional (3D) mapping,in accordance with an embodiment of the present invention. In thepresent example, system 20 comprises a scanning unit 21 composed of,inter-alia, a SEM column system (not shown), detection system (notshown) and a handling system (not shown) for handling samples, scanningthe samples using SEM and detecting signals indicative of, e.g., theshape, design, material and other features of the samples.

System 20 further comprises an image processing unit 23 that processesdigital images that are produced by detectors in scanning unit 21. Aswill be explained below, however, this sort of partitioning is notmandatory, and the functions of system 20 can be implemented in a singleunit or partitioned among multiple units as appropriate.

System 20 can be used in various applications, such as in CriticalDimension (CD) metrology, Defect Review (DR) or any other suitableapplication. In the embodiments described herein, the samples mapped bysystem 20 comprise semiconductor wafers. Alternatively, however, system20 can be used for 3D mapping of any other suitable type of sample, suchas semiconductor masks and reticles, flat display panels, solar panelsand more.

Scanning unit 21 in system 20 scans a sample 22, which has a certainheight profile or surface topography. For example, the sample maycomprise a patterned semiconductor wafer on which electronic components,conductors and other elements are disposed. Unit 21 irradiates sample 22using a beam of electrons, detects secondary electrons that are emittedfrom the sample in response to the irradiation, and uses the secondaryelectron detection to generate a 3D model of the sample surface usingmethods that are described in detail below.

Unit 21 in the present example comprises an electron source 24, whichirradiates sample 22 with a beam of Primary Electrons (PE). Typically,the PE beam irradiates a certain point on the sample surface at anygiven time, and the beam scans the sample, e.g., in a raster pattern. Inresponse to irradiation by the PE, Secondary Electrons (SE) are emittedfrom the irradiated point on the sample. The SE are emitted in variousangles and are detected by a detector array 28.

In the present embodiment, array 28 comprises a top detector 32A and twoside detectors 32B and 32C respectively denoted D1 and D2. The topdetector is positioned perpendicularly above the plane of the sample,whereas the side detectors are positioned at oblique angles relative tothe sample plane. An alternative detector configuration having four sidedetectors is shown in FIG. 2 below. An example technique of manipulatingthe outputs of the four side detectors is shown in FIG. 7 below. (Sample22, electron source 24 and array 28 are shown in the figure in a sideview. The configuration of detectors 32A . . . 32C in array 28, however,is shown in a top view for the sake of clarity.)

Each detector captures the SE in a certain range of angles relative tothe irradiation point. In the example of FIG. 1, top detector 32Acaptures the SE that are emitted within a certain conical sector whosevertex is the irradiation point. Each of side detectors 32B and 32Ccaptures the SE in a respective, different angular and energy sector.

Typically, the top detector is used for segmenting the image of thesample surface into regions of different material compositions, as willbe explained further below. The top detector is best suited for thistask since it is highly sensitive to material contrast, as opposed tothe side detectors that are more sensitive to topography contrast.Unlike oblique collection of SE, in normal collection of SE (asperformed by the top detector) each point in the collected image isaccurately indicative of a single irradiated point of the sample surfaceand less affected by contributions from the surroundings of theirradiated point.

Thus, when analyzing the output of the top detector, intensitydifferences that are not associated with edges of patterns are typicallyindicative of material composition differences. The disclosed techniquesthus generate material-related information and use this information forthe generation of a 3D model, e.g., height map, of a sample. Thematerial-related information is generated by processing signals producedby the top detector. Edge information is typically disregarded whenperforming material segmentation. Nevertheless, in alternativeembodiments, the top detector may also be used for other purposes.

In one example embodiment, electron source 24 comprises an electron gun,and each of detectors 32A . . . 32C comprises a combination of ascintillator and a Photo-Multiplier Tube (PMT). Detector array 28 ispositioned e.g. 120 mm above the sample, the diameter of top detector32A is e.g. on the order of 14 mm, and the external diameter of sidedetectors 32B and 32C is e.g. on the order of 25 mm. Theseimplementation details are given, however, purely by way of example. Inalternative embodiments any other suitable configuration can be used.Typically, each detector captures the SE in a certain respective rangeof angles and energies, determined by the geometry.

Each detector generates a signal that depends on the yield of secondaryelectrons within the angular sector captured by the detector. As the PEbeam scans the sample, each detector generates a signal that depends, asa function of time, on the SE yield within its respective angular sectorfrom the currently-irradiated point on the sample.

In the example of FIG. 1, image processing unit 23 produces a 3D model(e.g., height map) of the surface of sample 22, based on the signalsgenerated by detectors 32A . . . 32C. Unit 23 comprises an interface 37that receives the signals produced by the detectors, and a processor 38that carries out the mapping methods described herein. In particular,processor 38 calibrates the signals produced by the detectors such thatthe 3D model is unaffected by differences in material composition of thesample surface. Although the embodiments described herein refer mainlyto sample surfaces having two different material types, the disclosedtechniques can be used for mapping samples whose surfaces are made-up ofany desired number of material types.

In some embodiments, unit 23 comprises a storage device 39 for storingdigital representations of the detector outputs, the resulting heightmap, and/or any other suitable information. Typically, processor 38comprises a general-purpose computer, which is programmed in software tocarry out the functions described herein. The software may be downloadedto the computer in electronic form, over a network, for example, or itmay, alternatively or additionally, be provided and/or stored onnon-transitory tangible media, such as magnetic, optical, or electronicmemory.

FIG. 2 is a diagram that schematically illustrates a detector array, inaccordance with an alternative embodiment of the present invention. Inthe present example, the array comprises a top detector and fourquadrant side detectors denoted D1 . . . D4. The array of FIG. 2 can beused instead of array 28 in system 20. Further alternatively, system 20may comprise any other suitable number of detectors arranged in anyother suitable geometrical configuration. An example method ofmanipulating the outputs of detectors D1 . . . D4 is described in FIG. 7below.

The system configuration of FIG. 1 above is an example configuration. Inalternative embodiments, system 20 can be implemented in any othersuitable configuration. For example, the disclosed embodiments refer toconfigurations having two or four side detectors. The disclosedtechniques, however, are not limited to such configurations, andalternative embodiments may use any other suitable number of sidedetectors.

As another example, the disclosed techniques may be performed “on-tool,”i.e., by image processing unit 23 of system 20. In these embodiments,processor 38 carries out the disclosed mapping techniques, possiblyalong with other image processing functions of system 20. In alternativeembodiments, the disclosed techniques can be carried out by a separate,dedicated system or processor. System elements that are not mandatoryfor understanding of the disclosed techniques have been omitted from thefigure for the sake of clarity.

Geometrical Conventions

FIG. 3 is a diagram showing the geometrical conventions that are used inthe subsequent description. The particular geometrical notation usedherein is in no way limiting, and is used purely for the sake ofconceptual clarity.

Sample 22 is positioned in a certain plane relative to the x, y and zaxes. A vector n marks the normal to this plane. In other words, vectorn is perpendicular to sample 22. The inclination of the sample withrespect to the x-y plane, i.e., the angle between n and the z axis, isdenoted 8. The origin of the coordinate system (x=y=z=0) marks the pointat which the sample is irradiated with the PE beam at a given time. Thebeam irradiates the sample along the z axis, from top to bottom.

As a result of the irradiation, SE are emitted from the sample invarious directions. The yield y of SE depends on the tilt angle θ,typically in accordance with y=y(cos(θ)). The velocity vectors of theSE, denoted v, are typically distributed in accordance with Lambert'slaw, i.e., p∝<cos(φ), wherein φ denotes the angle between v and n.

3D Reconstruction of Height Profile Based on Multiple Detector Signals

Let H denote the height profile of sample 22, i.e., the height of thewafer surface as a function of location on the wafer. The signal levelproduced by the ith detector, denoted Ei, depends on the gradient of theheight profile, and on the relative direction between the detector andthe irradiation point. We can write:E _(i) =k _(i) ·Y ₀ ·R _(i)( g,{d ₁ ,d ₂, . . . })  [1]wherein g denotes the gradient of the height profile g=∇H, and d _(l)denotes the vector from the irradiation point to the l^(th) detector.R_(i) denotes a reflectance function, Y₀ denotes the total SE yield froma horizontal surface, and k denotes a machine-dependent constant.

For the case of two side detectors, the signals produced by thedetectors for a given irradiation point can be written as:E ₁ =E ₁( g,d ₁ ,d ₂),E ₂ =E ₂( g,d ₁ ,d ₂)  [2]

Once measured values of E1 and E2 are available from the detectors, thisequation system can be solved to derive the two components of the heightgradient g at the irradiation point. For a different number ofdetectors, a similar equation system can be defined and solved.

In some embodiments, processor 38 accepts the measured signal levels Eifrom the detectors, and solves equation system [2] to derive the heightgradient g. System 20 repeats this process for multiple irradiationpoints on sample 22, so as to produce a height gradient map of thesample. Then, processor 38 reconstructs the height profile H of thesample from the height gradient map, by implementing any suitablereconstruction method. Typically, processor 38 reconstructs the heightprofile by integrating the height gradient map in two dimensions.

The reflectance function R_(i) of the i^(th) detector can be written as:R _(i)( g,d )=Y(| g |)·η_(i)( g,d ₁ ,d ₂)  [3]wherein y denotes the total relative SE yield, and ηi denotes thefraction of SE captured by the ith detector. The term y(|g|) in Equation[3] is common to all detectors. The terms η_(i)(g, d ₁, d ₂) indicatethe relative distribution of captured SE among the different detectors.

In various embodiments, processor 38 may use various known models ofdependency of y on θ. In one example embodiment, processor 38 uses aninverse cosine dependence, i.e., y=1/cos θ. In another embodiment,processor 38 uses the dependence y=(cos θ)^(−α). In yet anotherembodiment, processor 38 uses the dependence y=(ξ−cos θ)/[1+(ξ−2)·cosθ]. Further alternatively, processor 38 may use any other suitabledependence of y on θ. Since y=y(cos(θ)), the term y(|g|) can be writtenas y(|g|)=y(√{square root over (1+|g|²)}).

In some embodiments, processor 38 computes each ii term in thereflectance function of Equation [3] by integrating the Lambertdistribution function over the angular sector (in φ/ψ polar coordinates)captured by the ith detector.

FIG. 4 is a diagram showing the geometrical notation used in integratingthe Lambert distribution function, in accordance with an exampleembodiment of the present invention. In this representation, a plane 44passes through the origin (the irradiation point) and is positionedsymmetrically with respect to detectors D1 and D2. In other words, plane44 passes through the origin and is orthogonal to the line connectingdetectors D1 and D2. The subspace that falls on the same side of plane44 as detector D1 is marked Ω1, and the subspace that falls on the sameside of plane 44 as detector D2 is marked Ω2.

A contour 40 marks the Lambertian that represents the spatialdistribution of secondary electron yield. A contour 52 marks theintersection of Lambertian 40 and plane 44. Angle 2ω denotes the apexangle of the conical sector that is captured by top detector 32A, i.e.,a fixed physical property of system 20. A contour 48 marks a dome thatis defined by the intersection of this conical sector and Lambertian 40.The part of dome 48 that falls on the D1 side of plane 44 is denoted T1,and the part of dome 48 that falls on the D2 side of plane 44 is denotedT2.

As can be seen from these definitions, integrating the Lambertdistribution function over the dome (i.e., over the interior of contour48) gives the secondary electron yield that is captured by the topdetector. Thus, η1 and η2 can be written as:

$\begin{matrix}{{\eta_{1} = {\underset{\Omega_{1} - T_{1}}{\int\int}\sin\;{\varphi cos}\;{\varphi \cdot {\mathbb{d}\varphi}}{\mathbb{d}\psi}}}{\eta_{2} = {\underset{\Omega_{2} - T_{2}}{\int\int}\sin\;{\varphi cos}\;{\varphi \cdot {\mathbb{d}\varphi}}{\mathbb{d}\psi}}}} & \lbrack 4\rbrack\end{matrix}$

Typically, processor 38 calculates the integrals of Equation [4]numerically, since there are usually no closed-forms expressions forthese integrals. Having calculated the reflectance function Ri ofEquation [3] above, processor 38 may solve Equation [3] to derive theheight gradient map g.

Calibration of 3D Mapping to Account for Surface Material

Up to this point, the above-described process did not take into accountdifferences in material composition across the surface of sample 22. Inmany practical scenarios, however, the surface of sample 22 comprisesdifferent features or structures that are made of different materials.For example, some regions of the surface may comprise substrate materialsuch as Silicon, while other regions may comprise metallic conductors,other semiconductor materials or any other suitable material.

As can be appreciated, the yield of secondary electrons in a particulardirection depends both on the height gradient and on the materialcomposition at the irradiation point. Consequently, signals E_(i)produced by the detectors of system 20 depend on these two factors, aswell. Unless accounted for, differences in material composition maydistort the estimation of the height gradient map g, and thereforedistort the 3D model of the sample calculated by system 20.

In some embodiments of the present invention, processor 38 carries out acalibration process that factors-out the material composition of thesample surface. The disclosed calibration process distinguishes betweenthe two factors affecting the SE yield—surface topography and surfacematerial. When using this calibration process, the resulting 3D model ofsample 22 is substantially unaffected by material compositiondifferences, and therefore better reproduces the sample surfacetopography.

The signal produced by the ith detector, Ei, is defined by Equation [1]above. The term R_(i)(g,{d ₁,d ₂,}) in Equation [1] depends only on thesurface topography. When the sample surface comprises differentmaterials, however, the term k_(i)·Y₀ in Equation [1] is unknowna-priori, and may vary from one irradiation point to another, since Y0depends on the type of material.

In some embodiments, processor 38 solves this problem by calibrating thereflectance function Ri for a given irradiation point to account for theactual material at that point. For a perfectly horizontal plane, we canwrite:y=1,η_(i)=η_(H)  [5]

wherein ηH denotes the fraction of SE captured from a horizontal plane—aconstant that depends on the detector geometry. The signal produced bythe ith detector in response to irradiating a horizontal plane is thusgiven by:E _(iH) =k _(i) ·Y ₀·η_(H)  [6]

Processor 38 may obtain EiH, for example, by choosing a referenceirradiation point on sample 22 that is known to be horizontal (g=0), andmeasuring the detector signals when this point is irradiated. Havingobtained E_(iH), processor 38 may derive k_(i)·Y₀ from Equation [6].This derivation gives the value of k_(i)·Y₀ for the specific material atthe reference (horizontal) irradiation point. Thus, the process ofchoosing reference irradiation points in the images and deriving E_(iH)should typically be repeated for each type of material that is presenton the sample surface.

When later measuring a given irradiation point, processor 38 normalizesthe reflectance function Ri with the EiH value that is applicable to thetype of material at the given irradiation point:

$\begin{matrix}{R_{i} = {\frac{E_{i}}{E_{iH}} \cdot \eta_{H}}} & \lbrack 7\rbrack\end{matrix}$

Since both Ei and EiH depend on the type of material, the normalized Ridepends only on surface topography and not on material. From thenormalized reflectance functions R_(i), processor 38 is able to derivethe height gradient g at the irradiation point. This derived value of gis independent of material type. The description that follows explainsan example scheme of deriving g from R_(i).

Thus, in the present context, the measured reference EiH values for thedifferent material types are regarded as calibration factors thatprocessor 38 applies to the detector outputs in computing the 3Dtopographical model of the sample surface. In alternative embodiment,processor 38 may compute and apply any other suitable kind ofcalibration factors that compensate for the differences in secondaryelectron yield of different materials.

It can be shown that Ri can be written as:R _(i) =y(| g |)·η_(i)(γ)  [8]

wherein γ is defined by:

$\begin{matrix}{{\gamma \equiv {\cos\left( {{\angle\;\overset{\_}{n}},{\Delta\;\overset{\_}{d}}} \right)}} = \frac{\left( {{\overset{\_}{g} \cdot \Delta}\;\overset{\_}{d}} \right)}{\sqrt{1 + {\overset{\_}{g}}^{2}}}} & \lbrack 9\rbrack\end{matrix}$

wherein n denotes a unit vector that is normal (perpendicular) to thesample surface at the irradiation point, and Δd denotes a unit vectoralong the line connecting the two side detectors. The term (g·Δd)denotes a scalar product of the two vectors.

It can be shown that the gradient g is given by:

$\begin{matrix}{{{{\overset{\_}{g}} = {y^{- 1}\left( \frac{R_{1}}{V_{1}\left( r_{12} \right)} \right)}},{\left( {\overset{\_}{g},{\Delta\;\overset{\_}{d}}} \right) = {{F^{- 1}\left( r_{12} \right)} \cdot \sqrt{1 + {\overset{\_}{g}}^{2}}}}}{wherein}} & \lbrack 10\rbrack \\{{r_{11} \equiv \frac{R_{1}}{R_{2}}} = {\left. {\frac{\eta_{1}(\gamma)}{\eta_{2}(\gamma)} \equiv {F(\gamma)}}\Rightarrow\gamma \right. = {F^{- 1}\left( r_{12} \right)}}} & \lbrack 11\rbrack \\{R_{1} = {{{y\left( {\overset{\_}{g}} \right)} \cdot {\eta_{1}\left( {F^{- 1}\left( r_{12} \right)} \right)}} = {{y\left( {\overset{\_}{g}} \right)} \cdot {V_{1}\left( r_{12} \right)}}}} & \lbrack 12\rbrack\end{matrix}$

In some embodiments, processor 38 calculates the two components of gfrom Equation [10]. The functions F-1 and V1 depend on ω (the apex angleof the conical sector captured by the top detector). Typically,processor 38 holds predefined tables of values of these functions, anduses the tables to evaluate the functions when calculating g.

FIG. 5 is a graph showing functions F-1 and V1 used in calculating aheight gradient map, in accordance with an example embodiment of thepresent invention. The top graph in the figure shows function V1 forvarious values of ω, and the bottom graph shows function F-1 fordifferent values of w. In alternative embodiments, e.g., for otherdetector geometries, any other suitable functions can be used.

In some embodiments, processor 38 calculates one component of the heightgradient g that is along the line connecting the two side detectors D1and D2, and another component of the gradient that is perpendicular tothis line. The two components are denoted g_(d) and g_(d⊥),respectively, and are given by:g _(d)=( g·Δd ),g _(d⊥)=±√{square root over (| g| ² −g _(d) ²)}  [13]

Note that the perpendicular gradient component g_(d⊥) is ambiguous,i.e., has two solutions that are theoretically possible. One possibleway to resolve this ambiguity is to use the integrability property ofgradient functions. Generally, the integral of a gradient function overa closed loop is zero:

$\begin{matrix}{C = {{\oint\limits_{S}\left( {\overset{\_}{g} \cdot {\mathbb{d}\overset{\_}{s}}} \right)} = 0}} & \lbrack 14\rbrack\end{matrix}$

wherein S may denote any closed loop path on the sample surface. Bychoosing a rectangular path with two sides parallel with g_(d) and twosides parallel with g_(d⊥), the requirement of Equation [14] can bewritten as:C=∫g _(d) ·dy−∫g _(d⊥) ·dx=0  [15]

From Equation [15] it can be seen that∫g _(d) ·dy>0

g _(d⊥)>0  [16]

In some embodiments, processor 38 tests both hypotheses (both thepositive value and the negative values of g_(d⊥) in Equation [13]) inthe test of Equations [15] and [16]. The hypothesis for which theintegral of Equation [15] is closer to zero is chosen as the correctvalue of g_(d⊥).

The above-described ambiguity resolution test may not function properlywhen the height profile slope is parallel to the line connectingdetectors D1 and D2. One possible solution is to position sample 22 suchthat its features are oriented obliquely relative to the line connectingthe detectors. In an example embodiment, the sample is placed such thatits axes are at a 45° angle (in the x-y plane) relative to the lineconnecting the detectors.

After computing the two components of gradient g at each irradiationpoint on the sample surface, processor 38 integrates the gradient in twodimensions to reconstruct the height map H of the sample. In practice,however, the computed gradient components may not be readily integrable,because they are often approximate and deviate from an ideal gradientfunction. Thus, the task of integrating the gradient can be regarded asthe task of finding a two-dimensional scalar map whose two-dimensionalgradient is as close as possible to the computed gradient. In someembodiments, processor 38 finds such a scalar map and outputs it as thereconstructed height map of the sample.

Various methods for fitting a scalar map to a given gradient map areknown in the art, and any such method can be used by processor 38. Anexample method is described by Frankot and Chellappa, in “A Method forEnforcing Integrability in Shape from Shading Algorithms,” IEEETransactions on Pattern Analysis and Machine Intelligence, Volume 10,No. 4, July, 1988, pages 439-451. According to this article, the heightmap is calculated by:

$\begin{matrix}{{F_{H}(\omega)} = \frac{{{- j}\;\omega_{x}F_{gx}} - {j\;\omega_{y}F_{gy}}}{\omega_{x}^{2} + \omega_{y}^{2}}} & \lbrack 17\rbrack\end{matrix}$

wherein F_(H)(ω) denotes the Fourier transform of the height map H, andF_(gx) and F_(gy) denote the Fourier transforms of the gradientcomponents.

3D Mapping Method Description

FIG. 6 is a flow chart that schematically illustrates a method for 3Dmapping of a sample, e.g. wafer sample 22 shown in FIG. 1, carried outby an inspection, metrology or review system, e.g. system 20 shown inFIG. 1, in accordance with an embodiment of the present invention. Themethod begins with system 20 scanning sample 22 with a beam of PrimaryElectrons (PE), at a scanning step 60. During the scan, detectors 32A .. . 32C detect the Secondary Electrons (SE) that are emitted from thesample for each irradiated point on the sample surface, at a detectionstep 64. Digital representations of the detector signals are provided toprocessor 38 of mapping unit 36 via interface 37.

Processor 38 produces multiple SEM images of the sample, one image pereach detector. The image of a given detector comprises a two-dimensionalarray of values that indicate the SE yield captured by that detectorfrom the various irradiated points on the sample surface. In the exampleconfiguration of FIG. 1, processor 38 produces three imagescorresponding to detectors 32A . . . 32C (the top detector plus two sidedetectors). Processor 38 uses these images to calculate the 3D heightmap of sample 22, taking into account and compensating for the types ofmaterial making up the sample surface.

In some embodiments, processor 38 divides the sample surface intosegments depending on the surface material, at a segmentation step 68.Each segment comprises the points on the sample surface that are made-upof a respective material. For example, one segment may comprise thelocations on the sample surface that are made-up of Silicon, and anothersegment may comprise the locations on the sample surface that aremade-up of metal conductors. Processor 38 may use any suitable imageprocessing scheme for carrying out this segmentation. The processor mayperform the segmentation based on any single image or based on multipleimages. In one embodiment, the processor uses the image of top detector32A for this purpose.

For each type of material, processor 38 identifies one or more regionson the sample surface that are substantially horizontal, at a regionidentification step 72. Processor 38 may identify the horizontal regionsin various ways. In an example embodiment, most of the sample surface ishorizontal, with the exception of feature edges that can be detected byprocessing one or more of the SEM images produced by the detectors.Processor 38 may identify edges in one of the images, and segment theimage using the identified edges. The processor may differentiatebetween horizontal regions made of different materials based on themeasured electron yield in each segment. Typically, although notnecessarily, the processor uses the image of top detector 32A for thispurpose.

For each type of material, processor 38 uses one or more points in thehorizontal regions of this material to estimate EiH, as explained abovewith respect to Equation [6]. The processor stores the estimated EiH ofeach material type for later use in calibration.

For each irradiated point on the sample surface, processor 38 calculatesthe gradient g of the height map based on the corresponding image pointsin the multiple images. In some embodiments, processor 38 calculates thereflectance functions Ri and calibrates them so as to factor out thetype of material using the pre-calculated EiH values, at a reflectancecalculation step 76. Processor 38 may calculate the reflectancefunctions for a given irradiation point by: (i) identifying the type ofmaterial at the given irradiation point, and (ii) normalizing thereflectance functions Ri for the given irradiation point using the EiHvalue of the identified material type.

Processor 38 then calculates the gradient map g from the normalizedreflectance functions Ri, at a gradient calculation step 80. Thecalculation may follow, for example, the process of Equations [8]-[13]above. At this stage, processor 38 has a gradient map of the sample thatis unaffected by the different material types. Processor 38 now derivesthe height map H of the sample from the gradient map, at a height mapderivation step 84. The derivation may follow, for example, the processof Equations [14]-[17] above. The height map is then provided as output.In some embodiments the height map can be presented to an operator usinga suitable Graphical User Interface (GUI). Additionally oralternatively, the height map can be provided to another system orapplication for subsequent processing, e.g., for measuring CriticalDimensions (CD) of the sample or for Defect Review (DR).

The embodiments described herein refer to calibration of the signalsproduced by the multiple detectors in order to factor-out the effect ofthe multiple materials making up the sample surface. In alternativeembodiments, however, the disclosed calibration schemes can be appliedto any suitable direct or indirect output of the detectors, such as tothe images produced by processor 38 from the detector signals.

FIG. 7 is a flow chart that schematically illustrates a method for 3Dmapping of a sample, in accordance with an alternative embodiment of thepresent invention. The method of FIG. 7 is used in conjunction with thefour side detector configuration of FIG. 2 above. In the presentexample, the method begins with processor 38 selecting pairs of sidedetectors, at a pairing step 90. Typically, the processor selects pairsof adjacent side detectors, e.g., D1+D2 and D3+D4.

Processor 38 combines the outputs (images) produced by the sidedetectors in each pair, at a pair combining step 94. In an embodiment,processor 38 repeats the pairing and combining process for differentpairs of side detectors, at a re-pairing step 98. For example, processor38 may initially (step 90) pair detectors D1+D2 and D3+D4, andsubsequently (step 98) pair detectors D1+D4 and D2+D3.

Processor 38 sums the results of the two pairing operations, at asummation step 102, to form a single composite image. Processor 38 thenprocesses this single image to produce a 3D height map of the sample, ata processing step 106. This processing may use, for example, the methodof FIG. 6 above.

FIG. 8 illustrates a diagrammatic representation of a machine in theexemplary form of a computer system 800 within which a set ofinstructions, for causing the machine to perform any one or more of themethodologies discussed herein, may be executed. In alternativeembodiments, the machine may be connected (e.g., networked) to othermachines in a local area network (LAN), an intranet, an extranet, or theInternet. The machine may operate in the capacity of a server or aclient machine in a client-server network environment, or as a peermachine in a peer-to-peer (or distributed) network environment. Themachine may be a personal computer (PC), a tablet PC, a set-top box(STB), a Personal Digital Assistant (PDA), a cellular telephone, a webappliance, a server, a network router, switch or bridge, or any machinecapable of executing a set of instructions (sequential or otherwise)that specify actions to be taken by that machine. Further, while only asingle machine is illustrated, the term “machine” shall also be taken toinclude any collection of machines that individually or jointly executea set (or multiple sets) of instructions to perform any one or more ofthe methodologies discussed herein. In one embodiment, computer system800 may be representative of a server, such as server 102, running imageconverter 110.

The exemplary computer system 800 includes a processing device 802, amain memory 804 (e.g., read-only memory (ROM), flash memory, dynamicrandom access memory (DRAM) (such as synchronous DRAM (SDRAM) or RambusDRAM (RDRAM), etc.), a static memory 806 (e.g., flash memory, staticrandom access memory (SRAM), etc.), and a data storage device 818, whichcommunicate with each other via a bus 830. Any of the signals providedover various buses described herein may be time multiplexed with othersignals and provided over one or more common buses. Additionally, theinterconnection between circuit components or blocks may be shown asbuses or as single signal lines. Each of the buses may alternatively beone or more single signal lines and each of the single signal lines mayalternatively be buses.

Processing device 802 represents one or more general-purpose processingdevices such as a microprocessor, central processing unit, or the like.More particularly, the processing device may be complex instruction setcomputing (CISC) microprocessor, reduced instruction set computer (RISC)microprocessor, very long instruction word (VLIW) microprocessor, orprocessor implementing other instruction sets, or processorsimplementing a combination of instruction sets. Processing device 802may also be one or more special-purpose processing devices such as anapplication specific integrated circuit (ASIC), a field programmablegate array (FPGA), a digital signal processor (DSP), network processor,or the like. The processing device 802 is configured to executeprocessing logic 826 for performing the operations and steps discussedherein.

The computer system 800 may further include a network interface device808. The computer system 800 also may include a video display unit 810(e.g., a liquid crystal display (LCD) or a cathode ray tube (CRT)), analphanumeric input device 812 (e.g., a keyboard), a cursor controldevice 814 (e.g., a mouse), and a signal generation device 816 (e.g., aspeaker).

The data storage device 818 may include a machine-readable storagemedium 828, on which is stored one or more set of instructions 822(e.g., software) embodying any one or more of the methodologies offunctions described herein. The instructions 822 may also reside,completely or at least partially, within the main memory 804 and/orwithin the processing device 802 during execution thereof by thecomputer system 800; the main memory 804 and the processing device 802also constituting machine-readable storage media. The instructions 822may further be transmitted or received over a network 820 via thenetwork interface device 808.

While the machine-readable storage medium 828 is shown in an exemplaryembodiment to be a single medium, the term “machine-readable storagemedium” should be taken to include a single medium or multiple media(e.g., a centralized or distributed database, and/or associated cachesand servers) that store the one or more sets of instructions. Amachine-readable medium includes any mechanism for storing informationin a form (e.g., software, processing application) readable by a machine(e.g., a computer). The machine-readable medium may include, but is notlimited to, magnetic storage medium (e.g., floppy diskette); opticalstorage medium (e.g., CD-ROM); magneto-optical storage medium; read-onlymemory (ROM); random-access memory (RAM); erasable programmable memory(e.g., EPROM and EEPROM); flash memory; or another type of mediumsuitable for storing electronic instructions.

The preceding description sets forth numerous specific details such asexamples of specific systems, components, methods, and so forth, inorder to provide a good understanding of several embodiments of thepresent invention. It will be apparent to one skilled in the art,however, that at least some embodiments of the present invention may bepracticed without these specific details. In other instances, well-knowncomponents or methods are not described in detail or are presented insimple block diagram format in order to avoid unnecessarily obscuringthe present invention. Thus, the specific details set forth are merelyexemplary. Particular implementations may vary from these exemplarydetails and still be contemplated to be within the scope of the presentinvention.

Reference throughout this specification to “one embodiment” or “anembodiment” means that a particular feature, structure, orcharacteristic described in connection with the embodiment is includedin at least one embodiment. Thus, the appearances of the phrase “in oneembodiment” or “in an embodiment” in various places throughout thisspecification are not necessarily all referring to the same embodiment.In addition, the term “or” is intended to mean an inclusive “or” ratherthan an exclusive “or.”

Although the operations of the methods herein are shown and described ina particular order, the order of the operations of each method may bealtered so that certain operations may be performed in an inverse orderor so that certain operation may be performed, at least in part,concurrently with other operations. In another embodiment, instructionsor sub-operations of distinct operations may be in an intermittentand/or alternating manner.

Although the embodiments described herein mainly address inspection ofsemiconductor wafers, the methods and systems described herein can alsobe used in other applications, such as in inspection of masks.

It will thus be appreciated that the embodiments described above arecited by way of example, and that the present invention is not limitedto what has been particularly shown and described hereinabove. Rather,the scope of the present invention includes both combinations andsub-combinations of the various features described hereinabove, as wellas variations and modifications thereof which would occur to personsskilled in the art upon reading the foregoing description and which arenot disclosed in the prior art. Documents incorporated by reference inthe present patent application are to be considered an integral part ofthe application except that to the extent any terms are defined in theseincorporated documents in a manner that conflicts with the definitionsmade explicitly or implicitly in the present specification, only thedefinitions in the present specification should be considered.

The invention claimed is:
 1. A method comprising: receiving information corresponding to a detection of electrons emitted from an irradiated surface of a sample comprising a plurality of types of materials; computing calibration factors to compensate for a variation in a yield of the electrons emitted among the plurality of types of materials of the sample; and calculating, by a processing device, a three-dimensional (3D) model of the surface of the sample based on the received information corresponding to the detection of electrons emitted from the irradiated surface of the sample and the calibration factors to compensate for the variation in the yield of the electrons emitted among the plurality of types of materials of the sample.
 2. The method of claim 1, wherein the information corresponding to the detection of electrons emitted corresponds to a plurality of detector outputs that are associated with different positions relative to the irradiated surface of the sample.
 3. The method of claim 1, wherein the calculating of the 3D model of the surface of the sample comprises: generating a surface height gradient of the surface of the sample; and integrating the surface height gradient.
 4. The method of claim 1, wherein the generating of the surface height gradient of the surface of the sample comprises: defining, for a given point on the surface of the sample, a set of equations corresponding to reflectance functions; and deriving a corresponding surface height gradient at the given point by solving the set of the equations.
 5. The method of claim 1, wherein the calculating of the 3D model comprises: applying the calibration factors to the information corresponding to the detection of electrons emitted from the irradiated surface of the sample to compensate for the plurality of types of materials of the sample.
 6. The method of claim 5, wherein applying the calibration factors comprises normalizing a reflectance function for a given detector associated with the detection of electrons emitted corresponding to a point on the surface of the material that comprises a material type by using a particular calibration factor of the calibration factors that is computed for the material type.
 7. The method of claim 1, wherein the information corresponding to the detection of electrons emitted from the irradiated surface of the sample comprises at least one Scanning Electron Microscope (SEM) image.
 8. A system comprising: a memory; and a processing device operatively coupled with the memory to: receive information corresponding to a detection of electrons emitted from an irradiated surface of a sample comprising a plurality of types of materials; compute calibration factors to compensate for a variation in a yield of the electrons emitted among the plurality of types of materials of the sample; and calculate a three-dimensional (3D) model of the surface of the sample based on the received information corresponding to the detection of electrons emitted from the irradiated surface of the sample and the calibration factors to compensate for the variation in the yield of the electrons emitted among the plurality of types of materials of the sample.
 9. The system of claim 8, wherein the information corresponding to the detection of electrons emitted corresponds to a plurality of detector outputs that are associated with different positions relative to the irradiated surface of the sample.
 10. The system of claim 8, wherein the calculating of the 3D model of the surface of the sample comprises: generating a surface height gradient of the surface of the sample; and integrating the surface height gradient.
 11. The system of claim 8, wherein the generating of the surface height gradient of the surface of the sample comprises: defining, for a given point on the surface of the sample, a set of equations corresponding to reflectance functions; and deriving a corresponding surface height gradient at the given point by solving the set of the equations.
 12. The system of claim 8, wherein the calculating of the 3D model comprises: applying the calibration factors to the information corresponding to the detection of electrons emitted from the irradiated surface of the sample to compensate for the plurality of types of materials of the sample.
 13. The system of claim 12, wherein applying the calibration factors comprises normalizing a reflectance function for a given detector associated with the detection of electrons emitted corresponding to a point on the surface of the material that comprises a material type by using a particular calibration factor of the calibration factors that is computed for the material type.
 14. The system of claim 8, wherein the information corresponding to the detection of electrons emitted from the irradiated surface of the sample comprises at least one Scanning Electron Microscope (SEM) image.
 15. A non-transitory machine-readable storage medium having data that, when accessed by a processing device, cause the processing device to: receive information corresponding to a detection of electrons emitted from an irradiated surface of a sample comprising a plurality of types of materials; compute calibration factors to compensate for a variation in a yield of the electrons emitted among the plurality of types of materials of the sample; and calculate, by the processing device, a three-dimensional (3D) model of the surface of the sample based on the received information corresponding to the detection of electrons emitted from the irradiated surface of the sample and the calibration factors to compensate for the variation in the yield of the electrons emitted among the plurality of types of materials of the sample.
 16. The non-transitory machine-readable storage medium of claim 15, wherein the information corresponding to the detection of electrons emitted corresponds to a plurality of detector outputs that are associated with different positions relative to the irradiated surface of the sample.
 17. The non-transitory machine-readable storage medium of claim 15, wherein the calculating of the 3D model of the surface of the sample comprises: generating a surface height gradient of the surface of the sample; and integrating the surface height gradient.
 18. The non-transitory machine-readable storage medium of claim 15, wherein the generating of the surface height gradient of the surface of the sample comprises: defining, for a given point on the surface of the sample, a set of equations corresponding to reflectance functions; and deriving a corresponding surface height gradient at the given point by solving the set of the equations.
 19. The non-transitory machine-readable storage medium of claim 15, wherein the calculating of the 3D model comprises: applying the calibration factors to the information corresponding to the detection of electrons emitted from the irradiated surface of the sample to compensate for the plurality of types of materials of the sample.
 20. The non-transitory machine-readable storage medium of claim 19, wherein applying the calibration factors comprises normalizing a reflectance function for a given detector associated with the detection of electrons emitted corresponding to a point on the surface of the material that comprises a material type by using a particular calibration factor of the calibration factors that is computed for the material type. 